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more sonorous. The result is that pianos tuned by ear and immediately checked with a machine tend to vary from one degree to another from the purely theoretical semitone (mathematically the 12th root of two) due to human error and perception. (If pleasing the ear is the goal of an aural tuning, then pleasing the math is the goal of a machine tuning.) This is thought to be because strings can vary somewhat from note to note and even from neighbors within a unison. This non-linearity is different from true falseness where a string creates false harmonics and is more akin to minor variations in string thickness, string sounding length or minor bridge inconsistencies.
40:
164:, and length. For instance, a stiff string under low tension (such as those found in the bass notes of small upright pianos) exhibits a high degree of inharmonicity, while a thinner string under higher tension (such as a treble string in a piano) or a more flexible string (such as a gut or nylon string used on a guitar or harp) will exhibit less inharmonicity. A wound string generally exhibits less inharmonicity than the equivalent solid string, and for that reason wound strings are often preferred.
273:
The inharmonicity in guitar strings can "cause stopped notes to stop sharp, meaning they will sound sharper both in terms of pitch and beating, than they "should". This is distinct from any temperament issue." Even if a guitar is built so that there are no "fret or neck angle errors, inharmonicity can make the simple approach of tuning open strings to notes stopped on the fifth or fourth frets" unreliable. Inharmonicity also demands that some of the "octaves may need to be compromised minutely."
28:
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sophisticated devices allow a technician to make custom inharmonicity measurementsâsimultaneously considering all partials for pitch and volume to determine the most appropriate stretch to employ for a given instrument. Some include an option to simply record a tuning that a technician has completed by ear; the technician can then duplicate that tuning on the same piano (or others of similar make and model) more easily and quickly.
175:, this means that the frequency of the harmonics increases linearly with the mode number. The added dispersion due to the stiffness, which is most prevalent in the thick bass strings, means that as the frequency increases, so too does the wave speed in the string. The result is that modes of the stiff string are no longer perfectly harmonic.
129:, the overtones are close toâor in some cases, quite exactlyâwhole number multiples of the fundamental frequency. Any departure from this ideal harmonic series is known as inharmonicity. The less elastic the strings are (that is, the shorter, thicker, smaller tension or stiffer they are), the more inharmonicity they exhibit.
297:
technique. However, this inharmonicity disappears when the strings are bowed, because the bow's stick-slip action is periodic, driving all of the resonances of the string at exactly harmonic ratios even if it has to drive them slightly off their natural frequency. As a result, the operating mode of a
284:
Some performers choose to focus the tuning towards the key of the piece, so that the tonic and dominant chords will have a clear, resonant sound. However, since this compromise may lead to muddy-sounding chords in sections of a piece that stray from the main key (e.g., a bridge section that modulates
227:
between tones. Piano tuners must deal with the inharmonicity of piano strings, which is present in different amounts in all of the ranges of the instrument, but especially in the bass and high treble registers. The result is that octaves are tuned slightly wider than the harmonic 2:1 ratio. The exact
239:
The issues surrounding setting the stretch by ear vs machine have not been settled; machines are better at deriving the absolute placement of semitones within a given chromatic scale, whereas non-machine tuners prefer to adjust these locations preferentially due to their temptation to make intervals
144:
counteracts the natural inharmonicity of the string or air column and causes the overtones to lock precisely onto integer multiples of the fundamental pitch, even though these are slightly different from the natural resonance points of the instrument. For this reason, a single tone played by a bowed
194:
In 1943, Schuck and Young were the first scientists to measure the spectral inharmonicity in piano tones. They found that the spectral partials in piano tones run progressively sharpâthat is to say, the lowest partials are sharpened the least and higher partials are progressively sharpened further.
280:
in the 1980s reached the mass market, it did not spell the end of tuning problems for guitarists. Even if an electronic tuner indicates that the guitar is "perfectly" in tune, some chords may not sound in tune when they are strummed, either due to string inharmonicity from worn or dirty strings, a
272:
While piano tuning is normally done by trained technicians, guitars such as acoustic guitars, electric guitars, and electric bass guitars are usually tuned by the guitarist themselves. When a guitarist tunes a guitar by ear, they have to take both temperament and string inharmonicity into account.
109:
Music harmony and intonation depends strongly on the harmonicity of tones. An ideal, homogeneous, infinitesimally thin or infinitely flexible string or column of air has exact harmonic modes of vibration. In any real musical instrument, the resonant body that produces the music toneâtypically a
235:
Because of the problem of inharmonicity, electronic piano tuning devices used by piano technicians are not designed to tune according to a simple harmonic series. Rather, the devices use various means to duplicate the stretched octaves and other adjustments a technician makes by ear. The most
198:
Inharmonicity is not necessarily unpleasant. In 1962, research by Harvey
Fletcher and his collaborators indicated that the spectral inharmonicity is important for tones to sound piano-like. They proposed that inharmonicity is responsible for the "warmth" property common to real piano tones.
281:
misplaced fret, a mis-adjusted bridge, or other problems. Due to the range of factors in play, getting a guitar to sound in tune is an exercise in compromise. "Worn or dirty strings are also inharmonic and harder to tune", a problem that can be partially resolved by cleaning strings.
263:
Another factor that can cause problems is the presence of rust on the strings or dirt in the windings. These factors can slightly raise the frequency of the higher modes, resulting in more inharmonicity.
110:
string, wire, or column of airâdeviates from this ideal and has some small or large amount of inharmonicity. For instance, a very thick string behaves less as an ideal string and more like a
203:
sounded more natural when some inharmonicity was introduced. In general, electronic instruments that duplicate acoustic instruments must duplicate both the inharmonicity and the resulting
520:
232:
in a piano tuning varies from piano to piano and even from register to register within a single pianoâdepending on the exact inharmonicity of the strings involved.
171:
of waves in a stiff string. In an ideal flexible string, the wave speed is constant as a function of frequency. Looking at the resonant frequency of a
247:
to minimize out-of-tuneness in the intervals and chords that will be played, and in terms of dealing with inharmonicity. For more information,
285:
a semitone down), some performers choose to make a broader compromise, and "split the difference" so that all chords will sound acceptable.
293:
Other stringed instruments such as the violin, viola, cello, and double bass also exhibit inharmonicity when notes are plucked using the
570:
931:
503:
172:
658:
629:, âString inharmonicity and the timbral quality of piano bass tones: Fletcher, Blackham, and Stratton (1962) revisited.â
156:, the string will exhibit inharmonicity. The inharmonicity of a string depends on its physical characteristics, such as
148:
However, when a string is struck or plucked, as with a piano string that is struck by its hammer, a violin string played
552:
90:
Acoustically, a note perceived to have a single distinct pitch in fact contains a variety of additional overtones. Many
59:
Percussion bars, such as xylophone, are hung at â2/9 and â7/9 length, and struck at 1/2 length, to reduce inharmonicity.
540:
611:
B. C. J. Moore, R.W. Peters, and B. C. Glasberg, âThresholds for the detection of inharmonicity in complex tones,â
532:
618:
F. Scalcon, D. Rocchesso, and G. Borin, âSubjective evaluation of the inharmonicity of synthetic piano tones,â in
114:(a tube of mass), which has natural resonances that are not whole number multiples of the fundamental frequency.
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bowed string playing a steady note is a compromise among the tunings of all of the (slightly inharmonic)
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76:
770:
302:, which is due to the strong non-linearity of the stick-slip action. Mode locking also occurs in the
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224:
521:"Audibility of Inharmonicity in String Instrument Sounds, and Implications to Digital Sound Systems"
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string instrument, brass instrument, or reed instrument does not necessarily exhibit inharmonicity.
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https://web.archive.org/web/20071015200222/http://www.amarilli.co.uk/guitar/howto.asp
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When strobe tuners became available in the 1970s, and then inexpensive
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Acoustical
Society of America - Large grand and small upright pianos
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How harmonic are harmonics? by Joe Wolfe, accessed 29 June 2008
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Proceedings of the
Society for Music Perception and Cognition
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Comparing harmonic (top) and inharmonic (bottom) waveforms.
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Piano tuning is a compromiseâboth in terms of choosing a
568:"Nonlinear Dynamics and Chaos in Musical Instruments"
219:, the technician sometimes listens for the sound of "
633:, MIT, Cambridge, Massachusetts, July - August 1997.
152:, or a guitar string that is plucked by a finger or
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167:The physical origin of this inharmonicity is the
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490:The Indian Musical Drums by Sir C V Raman 1930
185:Piano Acoustics - Inharmonicity and Piano Size
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117:However, in stringed instruments such as the
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615:vol. 77, no. 5, pp. 1861â1867, 1985.
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510:by Alexander Galembo and Lola L. Cuddy]
106:, create complex and inharmonic sounds.
83:multiples of the fundamental frequency (
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211:Inharmonicity leads to stretched tuning
35:(dashed gray lines indicate harmonics).
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533:The Cambridge companion to the piano
132:When a string is bowed or tone in a
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125:, or in some Indian drums such as
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613:Journal of the Acoust. Soc. Am.,
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622:ICMCâ98, pp. 53â56, 1998.
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190:Sound quality of inharmonicity
1:
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519:Matti A. Karjalainen (1999).
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207:of the original instruments.
140:or lips, a phenomenon called
620:Proc. Int. Comp. Music Conf.
566:Neville H. Fletcher (1994).
199:According to their research
7:
595:"What is a Sound Spectrum?"
577:. Complexity International.
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67:is the degree to which the
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388:Plucked string instruments
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173:string with two fixed ends
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215:When pianos are tuned by
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77:partials or partial tones
31:Inharmonic spectrum of a
329:Bowed string instruments
16:Not to be confused with
684:Architectural acoustics
531:Rowland, David (1998).
201:synthesized piano tones
136:initiated by vibrating
771:FletcherâMunson curves
766:Equal-loudness contour
676:Acoustical engineering
409:Approximately harmonic
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907:Hermann von Helmholtz
805:Fundamental frequency
709:Sympathetic resonance
230:octaves are stretched
94:instruments, such as
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927:Werner Meyer-Eppler
837:Missing fundamental
318:List of instruments
810:Frequency spectrum
573:2009-10-17 at the
506:2012-02-09 at the
429:Untuned percussion
323:Perfectly harmonic
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53:
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43:Harmonic spectrum.
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983:Musical acoustics
815:harmonic spectrum
347:Brass instruments
300:string resonances
278:electronic tuners
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912:Carleen Hutchins
844:Combination tone
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308:reed instruments
205:stretched tuning
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85:harmonic series
75:(also known as
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885:Acousticians
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423:Not harmonic
310:such as the
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257:Piano tuning
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892:John Backus
876:Subharmonic
729:Spectrogram
453:Subharmonic
396:harpsichord
304:human voice
245:temperament
69:frequencies
1028:Categories
978:Ultrasound
968:Infrasound
754:Bark scale
535:, p. 106.
459:References
169:dispersion
92:percussion
63:In music,
1034:Acoustics
859:Resonance
759:Mel scale
689:Monochord
668:Acoustics
295:pizzicato
225:roughness
162:stiffness
150:pizzicato
73:overtones
1013:Category
854:Overtone
822:Harmonic
627:L. Cuddy
571:Archived
504:Archived
437:See also
373:clarinet
359:trombone
312:clarinet
154:plectrum
112:cylinder
100:tam-tams
800:Formant
351:trumpet
306:and in
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158:tension
96:cymbals
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268:Guitar
179:Pianos
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119:violin
104:chimes
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988:Piano
973:Sound
787:pitch
749:Pitch
337:cello
127:tabla
81:whole
963:Echo
869:Node
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785:and
537:ISBN
402:...)
400:harp
369:oboe
355:horn
341:erhu
254:and
249:see
138:reed
33:bell
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